114 



NATURE 



[September 23, 1920 



of light. The following suggested examples may 

 perhaps be of interest. Ihey are not put forward as 

 possible "objections" to the theory, but with the 

 same intention as prompted the supposed "exceptions " 

 to the second law of thermodynamics. The latter, 

 although they did not disturb the application of the 

 law in its proi>er sphere, led to drastic limitations to 

 its general validity (e.g. the "sorting demons " of 

 Maxwell). 



Consider first a cube of unit volume, constructed of 

 rigid material absolutely impervious to heat. Sup- 

 pose the cube contains a gas the temperature of 

 which, measured by an observer rigidly attached to 

 the box, is T. What will be the temperature as 

 measured by another observer moving relative to the 

 first with a uniform velocitv v in the direction of one 

 of the edges of the cube? The volume of the cube 

 as measured by the second observer will, according to 

 the theory of relativity, be reduced to ij ■J \—v' jc'. If 

 the same laws hold for the gas for both observers, 

 the temper ature of the gas would seem to be 

 T(»J T.—v'jc')y-^. We note in passing that this 

 depends on y, the ratio of specific heats, and thus on 

 the structure of each of a definite number of molecules 

 of gas contained in the cube. If the gas is supposed 

 to be the mixture 2HI^H2+l2, the extent of dissocia- 

 tion depends only on the temperature and not on the 

 volume, and could be measured by the change in 

 intensity of a beam of light passed' through the box 

 in a direction at right angles to its motion, and 

 received by the second observer. The consideration of 

 the case in which the cube is at rest and the second 

 observer in motion would naturally follow. The 

 detailed consideration of this case would appear to 

 involve the transformation of the statistical equations 

 for the energy and entropy of the gas in terms of the 

 position and momentum co-ordinates of the molecules, 

 but I must defer detailed- discussion of this matter at 

 the moment. 



In the next case we will consider a possible defini- 

 tion of " simultaneity " not involving the use of ravs 

 of light. .\ chemical reaction taking place with a 

 measurable velocity in a given position as measured 

 by an observer at rest is employed. A solution is 

 divided into two equal parts. One remains with the 

 observer at rest, the other is taken by a second ob- 

 server anywhere he pleases. When an event occurs 

 simultaneously with respect to the two observers the 

 chemical reaction is stopped and the solutions are 

 brought back to the original position and analysed. 

 Let us say that if equal amounts of substance have 

 been changed the events w^ere simultaneous. What ob- 

 jection is raised to this definition ? .As a further case, 

 we may consider both observers provided with equal 

 weights of radium, and instructed to measure time 

 by counting the number of a-particles emitted from 

 a given instant. This change is found by experiment 

 to be independent of external conditions. If we 

 assume the use of rays of light as a standard method, 

 it follows that the rate of disintegration (and the rate 

 of a chemical reaction) will depend on the velocitv. .\ 

 possibility of testing this by-experiment with a centri- 

 fugal machine at once suggests itself. I find bv cal- 

 culation, however, that according to the theorv of 

 relativity the rate of emission of a-partic!es would not, 

 in the most favourable circumstances, be changed bv 

 more than about one particle per second per gram 

 of radium (see also A. H. Compton, Phil. Mag., 1920, 

 vol. xxxix., p. 659). 



.Attention may perhaps be directed to the calculation 

 of Bucherer (Physikal. Zeitsch., 1920, vol. xxi., p. 451), 

 who shows that the displacement of spectrum lines 

 mav be calculated without the assumption of a general 

 theory of relativity from the principles of thermo- 

 NO. 2656, VOL. 106] 



dynamics. The deflection of light by the sun may yet 

 be shown to depend on the condensation of ather — a 

 hypothesis first put forward by Newton (Boyle's 

 "Works," ed. by Birch, 1744, vol. i.). Neither of 

 these tests appears to be crucial. 



The possibility of an upper limit of temperature, 

 when a particle attains by thermal processes a velo- 

 city c, is complicated by the change of mass with 

 velocity. In the case of electrons it is further com- 

 plicated by the doubt as to whether they can be set 

 in motion at all by thermal means, which follows 

 from the values of the specific heats of metals at low 

 temperatures. J. R. Partington. 



East London College. 



Variations of Eucalyptus Foliage. 



The eucalyptus tree is a common object in the gardens 

 of Torquay, where it grows freely, though subject to 

 having its tender branch-ends killed occasionally by 

 frost-laden winds. • In the King's Gardens here there 

 are two of these trees of the same age which are 

 remarkable for the contrast in the appearance and 

 character of their foliage. One is bearing almost 

 entirely long scimitar-shaped leaves that are petiolate 

 and grow alternately on the branches with that pen- 

 dulous habit which so characterises these plants. Its 

 companion has a more robust appearance, and bears 

 only the more or less elongated heart-shaped leaves 

 that are erect, opposite, and sessile, with more of 

 the grey-blue gummy exudation that gives them the 

 common name of blue gum trees. It has been noticed 

 that this plant had lost its leading shoot when very 

 young, so that its mass is formed of branches grown 

 from lateral buds. A few trunk shoots have appeared 

 ihis season among the lower branches on the northern 

 side of the companion tree first mentioned that bear 

 the opposite, sessile leaves characteristic of the young 

 plants, and a recently pollarded tree in a private 

 garden near has developed two shoots from apparently 

 the same lateral bud on the north side of the tree, 

 that bear respectively the two forms of foliage, while a 

 sheltered and uninjured tree in the Terrace Gardens 

 of some 30 ft. in height has only the pendulous type 

 of leaf upon it. 



These observations, while bringing to notice a 

 remarkable instance of reversion to seedling or ances- 

 tral characters, seem to indicate that with these 

 plants light and temperature under the effects of 

 injury influence their development relative to tem- 

 porary or permanent reversion. 



Harford J. Lowe. 



The Museum, Torquay. 



Old Road Maps. 



The reference in Nature of September 16, p. 90, to 

 John Cary's old road map prompts me to send par- 

 ticulars of an old and rare book, " A Pocket-Guide to 

 the English Traveller : Being a Compleat Survey and 

 .Admeasurement of all the principal Roads and most 

 considerable cross Roads in England and Wales," by 

 Thomas Gardner, 1719. There are one hundred 

 copper-plate engravings showing the roads, with the 

 bridges, woods, inns, churches, beacons, gallows, etc., 

 passed en route. The scale is, for the actual roads, 

 about one inch to the mile, and every mile is num- 

 bered. This book has been in my possession for more 

 than fortv vears, and I have never met anyone who 

 has seen another copy. It is dedicated to " His Most 

 Serene Majesty George, King of Great Britain, France 

 and Ireland, etc." C. Carus-Wilson. 



September 17. 



